CN108376208B - Auxiliary anode system optimization method for grounding grid cathode protection - Google Patents

Auxiliary anode system optimization method for grounding grid cathode protection Download PDF

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CN108376208B
CN108376208B CN201810345321.3A CN201810345321A CN108376208B CN 108376208 B CN108376208 B CN 108376208B CN 201810345321 A CN201810345321 A CN 201810345321A CN 108376208 B CN108376208 B CN 108376208B
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宋春峰
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Shaanxi Huatian Juneng Technology Co ltd
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Abstract

The invention discloses an auxiliary anode system optimization method for grounding grid cathodic protection, which relates to the fields of electrical engineering, safety technology and anticorrosion protection, and comprises the following steps: s1, obtaining an auxiliary anode optimization design finite element mathematical model formula, S2, initializing the auxiliary anode optimization design finite element mathematical model formula, and making S (0) be S0I is 0, initial temperature T0100; s3, making T ═ TiWith T and SiCalling Metropolis sampling algorithm, and returning the state S as the current solution Si(ii) S, where i is the current time; s4, making T ═ Ti+1＝0.9TiI is i + 1; s5, checking whether the termination condition is satisfied
Figure DDA0001631726750000011
If so, the current solution SiTaking the solution as the optimal solution of the finite element model, otherwise, turning to the step S3; by the method, psi [ phi ] can be determined when the anode size, the position, the number and the specific values of the grounding grid specification are determinede，De(xe，ye，he)，L(a，b)，ne]A minimum value can be achieved.

Description

Auxiliary anode system optimization method for grounding grid cathode protection
Technical Field
The invention relates to the fields of electrical engineering, safety technology and anticorrosion protection, in particular to an auxiliary anode system optimization method for grounding grid cathodic protection.
Background
The transformer substation grounding grid is a necessary facility for working grounding, lightning grounding and protective grounding, is an important link for ensuring personal safety, equipment safety and system safety, and plays a role in discharging and equalizing lightning, static and fault current. When an accident occurs, if the grounding grid has defects, the short-circuit current cannot be fully diffused in the soil, so that the potential of the grounding grid is increased, the metal shell of the grounding equipment is provided with high voltage, personal safety is endangered, the insulation of a secondary protection device is broken down, even the equipment is damaged, the accident is enlarged, and the stability of a power grid system is damaged. The forced current cathodic protection is an effective grounding grid protection system. How to optimize the cathode protection effect of the forced current is of great importance in designing parameters of the auxiliary anode system of the grounding grid.
And existing butt jointsThe parameter design of the ground screen auxiliary anode system is realized based on a finite element circulation algorithm, and the main steps comprise: deriving an auxiliary anode optimization design finite element mathematical model for n from a model of a cathodic protection systemeAt an anode position De(xe,ye,he) Size of anode phieN number of anodeseAnd the specifications L (a, b) of the grounding grid to be protected, and four layers of circulation are set. In the first layer of circulation, the number of anodes is increased according to a specific rule and gradually increased (for example, the number of anodes can be 1, 2, 3, 4, and the like, which are sequentially increased); in the second layer cycle, each anode position De(xe,ye,he) Continuously changing according to a specific rule; making the anode size phi in the third layer of cycleeThe amplitude of (a) is changed according to a specific rule; in the fourth layer circulation, the grounding grid specification L (a, b) is changed continuously. The advantage of the calculation program of the circular algorithm is that psi phi can be obtained quicklye,De(xe,ye,he),L(a,b),ne]The change rule of the anode size, the position, the number and the grounding grid specification; the disadvantages are that the anode size, position, number and size of the grounding grid are not flexible enough, and when it is difficult to determine the specific values, psi [ phi ] & lte,De(xe,ye,he),L(a,b),ne]A minimum value can be achieved.
In summary, the existing method for optimizing the auxiliary anode system for the cathodic protection of the grounding grid has the disadvantages that the size, the position, the number of anodes and the specification of the grounding grid are not flexible enough, and when it is difficult to determine the specific values of the anodes, psi [ phi ]e,De(xe,ye,he),L(a,b),ne]A minimum value can be achieved.
Disclosure of Invention
The embodiment of the invention provides an auxiliary anode system optimization method for grounding grid cathodic protection, which is used for solving the problems that the size, the position, the number and the specification of a grounding grid are not flexible enough in the prior art, and when the specific values are difficult to determine, psi [ phi ]e,De(xe,ye,he),L(a,b),ne]The problem of the minimum value can be achieved.
The embodiment of the invention provides an auxiliary anode system optimization method for grounding grid cathodic protection, wherein during transformer substation grounding grid cathodic protection, an auxiliary anode is connected with a cathodic protection power supply and used for protecting the stability of a power grid system, and the method is characterized in that the grounding grid auxiliary anode system parameter optimization method based on simulated annealing finite elements is introduced into transformer substation grounding grid cathodic protection, and specifically comprises the following steps:
s1, obtaining a finite element mathematical model formula of the auxiliary anode optimization design;
s2, initializing a finite element mathematical model formula of the auxiliary anode optimization design, and taking Si＝Ψ[φe,De(xe,ye,he),L(a,b),ne]Simultaneously, let S (0) become SiI is 0, initial temperature T0＝100；
S3, making T ═ TiWith T and SiCalling a Metropolis sampling algorithm;
s4, solving a return state S based on the Metropolis sampling algorithm, and taking the return state S as a current solution Si(ii) S, where i is the current time;
s5, making T ═ Ti+1＝0.9Ti，i＝i+1；
S6, checking whether the termination condition is satisfied
Figure BDA0001631726730000021
If yes, go to step S7, otherwise go to step S3;
s7, solving the current SiThe optimal solution of the finite element model is used as the optimal solution of the finite element model, and the optimal solution of the finite element model is output; wherein the finite element model optimal solution is psi [ phi ]e,De(xe,ye,he),L(a,b),ne]The anode size, anode position and anode number at the time of obtaining the minimum value are obtained.
Preferably, the auxiliary anode optimal design finite element mathematical model formula is as follows:
Figure BDA0001631726730000031
wherein D ise(xe,ye,he) Is the buried position of the anode, [ phi ]eIs an anode potential, neA limiting value of the position of a coordinate source point of a jth anode point of a grounding grid in the model, xe,ye,heRespectively the projection of the anode on the X axis, the Y axis and the Z axis; l (a, b) is the specification of the grounding grid to be protected, neThe number of anodes; phi is apTo protect the potential, phipThe value depends on the characteristics of the protected metal structure and medium, the grounding grid has n nodes, and the potential phi at each nodejThe vector formed is [ phi ]1,φ2,…,φn]TMemory for recording
Figure BDA0001631726730000032
And Ψ1And Ψ2Is defined as:
Figure BDA0001631726730000033
Figure BDA0001631726730000034
wherein in the formulae (2) and (3), Ψ1Indicating the degree of uniformity of the potential distribution, /)2Indicating the closeness of the calculated value of the mean potential to the theoretical optimum, a1，α2As a weighting coefficient, satisfies 0. ltoreq. alpha1≤1，0≤α2Alpha is less than or equal to 11+α2＝1。
Preferably, the parameters of the established grounding grid auxiliary anode system are respectively: phi is ae＝20V，xe＝0,ye＝0,he＝0，a＝10cm,b＝10cm，ne＝1。
Preferably, solving for the return state S based on the Metropolis sampling algorithm includes:
(1) initializing, making k equal to 0, and solving S (k) equal to S currentlyiAt a temperature TThe following steps;
(2) generating a neighbor subset N (S (k)) + S according to the state S of the current solution S (k), randomly obtaining a new state S ' from N (S (k)) as a next candidate solution, and calculating the energy difference deltaC ' ═ C (S ') -C (S (k));
(3) if Δ C '< 0, accepting S' as the next current solution; if Δ C ' is greater than or equal to 0, accepting S ' as the next current solution with probability exp (- Δ C '/T);
(4) if S 'is accepted, let S (k +1) become S', otherwise S (k +1) become S (k);
(5) k +1, checking whether the termination condition is satisfied
Figure BDA0001631726730000041
If yes, executing the step (6), otherwise, executing the step (2);
(6) and returning to S (k) and ending.
In the embodiment of the invention, an auxiliary anode optimization design finite element mathematical model is carried out according to a physical model of ground net cathodic protection, for the auxiliary anode optimization design finite element mathematical model, on the basis of finite element simulation, a ground net cathodic protection system optimization algorithm based on a simulated annealing algorithm is provided, the algorithm ingeniously converts a multi-objective optimization problem into a single-objective optimization problem, reduces the complexity of the problem, finds the influence relationship of different positions of an anode on the surface potential of a ground net in the optimization process, and further finds the distribution rule of the anode positions and the surface potential of the ground net, thereby determining psi [ phi ] phi when the size, the positions, the number of the anode and the specific specification of the ground net are set to be specifice,De(xe,ye,he),L(a,b),ne]A minimum value can be achieved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of an auxiliary anode system optimization method for ground grid cathodic protection according to an embodiment of the present invention;
FIG. 2 is a model of the grounding grid cathodic protection provided by an embodiment of the present invention;
FIG. 3 is a finite element subdivision of the surface of a ground plane provided by an embodiment of the present invention;
FIG. 4 is a graph of potential distribution provided by an embodiment of the present invention;
FIG. 5 is a diagram illustrating distribution of grounding grid potential at different positions when the anode potential is 90V according to an embodiment of the present invention.
Detailed Description
An embodiment of the present invention will be described in detail below with reference to the accompanying drawings, but it should be understood that the scope of the present invention is not limited to the embodiment.
The method for optimizing the parameters of the grounding grid auxiliary anode system based on the simulated annealing finite element is introduced into the grounding grid cathodic protection of the transformer substation, and fig. 1 exemplarily shows a flow chart of the method for optimizing the auxiliary anode system of the grounding grid cathodic protection, and specifically comprises the following steps:
and S1, obtaining a finite element mathematical model formula of the auxiliary anode optimization design.
Wherein the finite element mathematical model formula is
Figure BDA0001631726730000051
Wherein D ise(xe,ye,he) Is the buried position of the anode, [ phi ]eIs an anode potential, neA limiting value of the position of a coordinate source point of a jth anode point of a grounding grid in the model, xe,ye,heRespectively the anode is on the X-axis, the Y-axis and the Z-axisAnd (5) projecting. L (a, b) is the specification of the grounding grid to be protected, neThe number of anodes. Phi is apTo protect the potential, phipThe value depends on the characteristics of the protected metal structure and medium, the grounding grid has n nodes, and the potential phi at each nodejThe vector formed is [ phi ]1,φ2,…,φn]TMemory for recording
Figure BDA0001631726730000052
And Ψ1And Ψ2Is defined as:
Figure BDA0001631726730000061
Figure BDA0001631726730000062
wherein in the formulae (2) and (3), Ψ1Indicating the degree of uniformity of the potential distribution, /)2Indicating how close the calculated value of the average potential is to the theoretical optimum value. Alpha is alpha1，α2As a weighting coefficient, satisfies 0. ltoreq. alpha1≤1，0≤α2Alpha is less than or equal to 11+α2＝1。
(1) Mathematical modeling of assisted anode optimization design
The auxiliary anode is an important component of the cathodic protection system, while the cathodic protection of the grounding grid is complex, and the model diagram is shown in fig. 2, so that the potential distribution of the protected body is uniform, and the design parameters of the anode are very important.
At present, in practical application, the burying position of the station is mainly determined by experience or field test, and in an operating station cathode protection system, due to improper position selection, a far protective body cannot be protected, and a near protective body can be over-protected; the result is that the auxiliary anode is re-addressed and buried, which is neither scientific nor economical. Theoretical and experimental researches on design parameters of the auxiliary anode show that reasonable anode design parameters can meet the requirement of potential distribution and ensure lower current density.
According to the design of cathode protection, all protected bodies are enabled to reach the protection potential, and for the purpose of corrosion protection of the protected metal component, the surface potential phi of the protected metal should satisfy the following conditions:
φ≤φp (4)
wherein phi ispTo protect the potential, phipThe value depends on the characteristics of the protected metal structure and the medium, the grounding grid has n nodes, and the surface potential of all protected bodies in the region can meet the requirements through two ways, namely: firstly, reasonably arranging and adjusting the position of an anode; and secondly, adjusting the current output of the anode. The adjustment of the anode current output is easy to realize in engineering, and only the current output of the current source is required to be adjusted. The burying of the anode in the construction requires a large investment and a large amount of work (excavation of earth, laying of a carbon bed, etc.), and thus it is almost impossible to adjust the position once fixed. Therefore, the research objective is to determine the optimal anode burying position during the design of the anticorrosion scheme before construction.
The finite element method can be used for solving the model, and potential values of each node on the surface of the cathode can be obtained on the selected grid.
The grounding grid has n nodes, and the potential phi at each nodejThe vector formed is [ phi ]1,φ2,…,φn]TMemory for recording
Figure BDA0001631726730000071
Defining:
Figure BDA0001631726730000072
Figure BDA0001631726730000073
of the two functions defined above, Ψ1Indicating the degree of uniformity of the potential distribution, /)2Indicating how close the calculated value of the average potential is to the theoretical optimum value.
The following anode optimization problem is presented: to find
Figure BDA0001631726730000074
Satisfy the requirement of
Figure BDA0001631726730000075
Thus, the optimization problem of the position, the size and the number of the anodes is expressed as a multi-objective planning problem.
It is significantly different from the counter-problem proposition commonly encountered in cathodic protection: first, it is not a single-objective planning problem, but rather a multi-objective planning with two objectives; second, the functional in the objective function is not defined in terms of the difference between the observed and calculated values, but rather is defined only by the calculated values. Since the concepts of mean and variance are borrowed from the definition of two objective functions, the inverse problem model is not called a mean variance model of partial differential equation inverse problem.
The idea of solving the inverse problem model is as follows:
firstly, a weighted average method is utilized to solve a multi-target planning problem into a single-target planning problem, and the order is as follows:
Figure BDA0001631726730000076
to find
Figure BDA0001631726730000077
Satisfies the following conditions:
Figure BDA0001631726730000078
second, in solving this inverse problem, it is necessary to continually solve a given set of [ φ ]e,De(xe,ye,he),L(a,b),ne]Solving the above equation model, which is in fact a process of solving the positive problem repeatedly.
Aiming at the characteristics, a calculation program for solving the inverse problem is designed by utilizing a finite element method. The calculation procedure can be divided into two parts: the core of the program and the processing of the calculation data.
The core part of the program is to solve the mathematical model using finite elements.
The data processing part of the program calculates an objective function by using the potential values of nodes on the cathode surface
Figure BDA0001631726730000081
The value of (c).
In the process of solving the inverse problem, the position and the size of the anode need to be frequently changed, and the solving area needs to be frequently subdivided.
To sum up, the finite element mathematical model for the auxiliary anode optimization design is formula (1), which is the basis of the SAOA:
Figure BDA0001631726730000082
in the formula, R represents a limit value of the position of the coordinate source point of the jth anode point of the grounding grid in the model.
Objective function
Figure BDA0001631726730000083
The variables are in indirect implicit function relation, so that the selected optimization algorithm is required to avoid calculating the derivative of the objective function and the constraint function in the calculation process, only the function values of the objective function and the constraint function are used, and therefore the intelligent optimization method is attempted by adopting a simulated annealing algorithm. The simulated annealing algorithm is essentially an intelligent optimization method, is directly oriented to optimization problems, and has a series of advantages compared with the traditional optimization method, the result of the method is a group of good solutions instead of a single solution, and the method provides a selectable opportunity for a user of the solution, so the method is particularly suitable for processing complex nonlinear optimization problems in engineering.
S2, initializing a finite element mathematical model formula of the auxiliary anode optimization design, and taking Si＝Ψ[φe,De(xe,ye,he),L(a,b),ne]Simultaneously, let S (0) become SiI is 0, initial temperature T0＝100；。
The parameters of the established auxiliary anode system of the grounding grid are respectively as follows: phi is ae＝20V，xe＝0,ye＝0,he＝0，a＝10cm,b＝10cm，ne＝1。
S3, making T ═ TiWith T and SiCalling Metropolis sampling algorithm, and returning the state S as the current solution SiWhere i is the current time.
S4, solving a return state S based on the Metropolis sampling algorithm, and taking the return state S as a current solution SiWhere i is the current time.
S5, making T ═ Ti+1＝0.9Ti，i＝i+1。
S6, checking whether the termination condition is satisfied
Figure BDA0001631726730000091
If yes, go to step S7, otherwise go to step S3.
S7, solving the current SiThe optimal solution of the finite element model is used as the optimal solution of the finite element model, and the optimal solution of the finite element model is output; optimal solution of finite element model is psi phie,De(xe,ye,he),L(a,b),ne]The anode size, anode position and anode number at the time of obtaining the minimum value are obtained.
Wherein the Metropolis sampling algorithm is described as follows:
(1) initializing, making k equal to 0, and solving S (k) equal to S currentlyiThe following steps are carried out at a temperature T.
(2) And generating a neighbor subset N (S (k)) + S according to the state S of the current solution S (k), randomly obtaining a new state S ' from N (S (k)) as a next solution candidate, and calculating the energy difference deltaC ' -C (S ') -C (S (k)).
(3) If Δ C '< 0, S' is accepted as the next current solution. If Δ C ' ≧ 0, S ' is accepted as the next current solution with probability exp (- Δ C '/T).
(4) And if S 'is received, making S (k +1) S', otherwise S (k +1) S (k).
(5)、k＝k+1, checking whether a termination condition is satisfied
Figure BDA0001631726730000092
If yes, executing the step (6), otherwise, executing the step (2).
(6) And returning to S (k) and ending.
The embodiment verification is carried out based on the auxiliary anode system optimization method for the grounding grid cathodic protection; taking the grounding grid 200m × 200m as an example, when the optimum potential phi is takenp-0.9V, weighting factor α1＝0.6、α2Fig. 3 shows a schematic diagram of the surface of the ground net after being split by the cathodic protection model according to the above SAOA algorithm when the value is 0.4.
Calculating by using an SAOA algorithm to obtain the optimal solution when the grounding grid cathodic protection system obtains the optimal protection effect as follows: anode potential phie93.6V; number of anodes ne3; the positions of the three anodes are A (0,156.8,83.7), B (132.6,0,78.6) and C (200, 64.2), respectively. At this time, the distribution of the surface potential of the grounding grid is shown in FIG. 4, the maximum potential of the surface of the grounding grid is-0.85V, and the minimum potential is-1.25V, which meets the engineering requirements. Fig. 4 shows the distribution of the surface potential of the grounding grid in three-dimensional space, and the potential becomes smaller gradually.
According to the SAOA algorithm, when the anode potential is phieAnd (5) respectively placing the anodes at positions 5-50 meters below the grounding grid, and obtaining the potential distribution of the grounding grid caused by different positions as shown in fig. 5. As can be seen from fig. 4, the average potential and variance of the surface of the ground grid become smaller as the burying depth of the anode increases.
The grounding grid is solved by using finite element simulated annealing algorithm (SAOA, variable-scale process (DFP) and Genetic Algorithm (GA) respectively, and the optimization calculation results of various algorithms are shown in Table 1.
Table 1 comparison of results of three algorithms (%)
Figure BDA0001631726730000101
As can be seen from table 1, in the optimization method of the ground grid cathodic protection system, the design accuracy based on the simulated annealing algorithm is improved by 1.12% compared with the design accuracy based on the genetic algorithm, and is improved by 1.64% compared with the design accuracy based on the variable-scale method.
The method carries out mathematical modeling according to a physical model of the grounding grid cathodic protection, and for the model, on the basis of finite element simulation, provides a grounding grid cathodic protection system optimization algorithm (SAOA) based on a simulated annealing algorithm, and the algorithm skillfully converts a multi-objective optimization problem into a single-objective optimization problem, thereby reducing the complexity of the problem. In the optimization process, the influence relationship of different positions of the anode on the surface potential of the grounding grid is found, and the distribution rule of the anode position and the surface potential of the grounding grid is further found. Experiments and simulations show that the algorithm is superior to the traditional AG algorithm and DFP method, the SAOA algorithm can obtain the global optimal solution with higher probability, and the result is a group of optimal solutions instead of a single solution, thereby providing selectable opportunities for users. The method has the advantages of strong robustness, global convergence, implicit parallelism and wide adaptability, can process different types of optimization design variables, and has no requirements on target functions and constraint functions. By comparing the superiority of this algorithm over the variable-scale method and the genetic algorithm, it is practically feasible.
In the embodiment of the invention, an auxiliary anode optimization design finite element mathematical model is carried out according to a physical model of ground net cathodic protection, for the auxiliary anode optimization design finite element mathematical model, on the basis of finite element simulation, a ground net cathodic protection system optimization algorithm based on a simulated annealing algorithm is provided, the algorithm ingeniously converts a multi-objective optimization problem into a single-objective optimization problem, reduces the complexity of the problem, finds the influence relationship of different positions of an anode on the surface potential of a ground net in the optimization process, and further finds the distribution rule of the anode positions and the surface potential of the ground net, thereby determining psi [ phi ] phi when the size, the positions, the number of the anode and the specific specification of the ground net are set to be specifice,De(xe,ye,he),L(a,b),ne]A minimum value can be achieved.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (3)

1. An auxiliary anode system optimization method for grounding grid cathodic protection comprises the following steps: during the protection of transformer substation's ground net negative pole, supplementary positive pole is connected with the cathodic protection power for the stability of protection grid system, its characterized in that will be based on the supplementary positive pole system parameter optimization method of ground net of simulated annealing finite element and introduce transformer substation's ground net cathodic protection, specifically include:
s1, obtaining a finite element mathematical model formula of the auxiliary anode optimization design;
s2, initializing a finite element mathematical model formula of the auxiliary anode optimization design, and taking Si＝Ψ[φe,De(xe,ye,he),L(a,b),ne]Simultaneously, let S (0) become SiI is 0, initial temperature T0＝100；
S3, making T ═ TiWith T and SiCalling a Metropolis sampling algorithm;
s4, solving a return state S based on the Metropolis sampling algorithm, and taking the return state S as a current solution Si(ii) S, where i is the current time;
s5, making T ═ Ti+1＝0.9Ti，i＝i+1；
S6, checking whether the termination condition is satisfied
Figure FDA0003063762570000011
If yes, go to step S7, otherwise go to step S3;
s7, solving the current SiThe optimal solution of the finite element model is used as the optimal solution of the finite element model, and the optimal solution of the finite element model is output; wherein the finite element model optimal solution is psi [ phi ]e,De(xe,ye,he),L(a,b),ne]Obtaining the size, position and number of anodes of the minimum value;
the auxiliary anode optimization design finite element mathematical model formula is as follows:
Figure FDA0003063762570000012
wherein D ise(xe,ye,he) Is the buried position of the anode, [ phi ]eIs an anode potential, neA limiting value of the position of a coordinate source point of a jth anode point of a grounding grid in the model, xe,ye,heRespectively the projection of the anode on the X axis, the Y axis and the Z axis; l (a, b) is the specification of the grounding grid to be protected, wherein a and b represent the length and the width of a main line of the grounding grid respectively; n iseThe number of anodes; phi is apTo protect the potential, phipThe value depends on the characteristics of the protected metal structure and medium, the grounding grid has n nodes, and the potential phi at each nodejThe vector formed is [ phi ]1,φ2,…,φn]TMemory for recording
Figure FDA0003063762570000021
And Ψ1And Ψ2Is defined as:
Figure FDA0003063762570000022
Figure FDA0003063762570000023
wherein in the formulae (2) and (3), Ψ1Indicating the degree of uniformity of the potential distribution, /)2Indicating the closeness of the calculated value of the mean potential to the theoretical optimum, a1，α2As a weighting coefficient, satisfies 0. ltoreq. alpha1≤1，0≤α2Alpha is less than or equal to 11+α2＝1。
2. The method for optimizing the auxiliary anode system for grounding grid cathodic protection of claim 1, wherein the parameters of the established auxiliary anode system of the grounding grid are respectively: phi is ae＝20V，xe＝0,ye＝0,he＝0，a＝10cm,b＝10cm，ne＝1。
3. The method of claim 1, wherein solving for a return state S based on the Metropolis sampling algorithm comprises:
(1) initializing, making k equal to 0, and solving S (k) equal to S currentlyiCarrying out the following steps at a temperature T;
(2) generating a neighbor subset N (S (k)) + S according to the state S of the current solution S (k), randomly obtaining a new state S ' from N (S (k)) as a next candidate solution, and calculating the energy difference deltaC ' ═ C (S ') -C (S (k));
(3) if Δ C '< 0, accepting S' as the next current solution; if Δ C ' is greater than or equal to 0, accepting S ' as the next current solution with probability exp (- Δ C '/T);
(4) if S 'is accepted, let S (k +1) become S', otherwise S (k +1) become S (k);
(5) k +1, checking whether the termination condition is satisfied
Figure FDA0003063762570000024
If yes, executing the step (6), otherwise, executing the step (2);
(6) and returning to S (k) and ending.
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